# A man repays a loan of $3250 by paying $20 in the first month and then increases the payment by $15 every month. How long will it take him to clear the loan?

##### 1 Answer

Nov 29, 2016

Define

We have:

At the end of the n-th month the total payment is:

Using Gauss' formula for the sum of the first

express this as an equation in

Solve for

Obviously we discard the negative solution and

So the debt is repaid at the end of the 20-th month.